Focus: Metamaterials Probe Changes in Spacetime Structure

Theorists propose that a nanostructured material could show what happens when the structure of spacetime changes, as some cosmologists have suggested may have occurred in the early universe.

At the time of the big bang, our universe may not have had exactly three dimensions of space and one of time, according to some theorists. In the 6 August Physical Review Letters, a team proposes a way to observe the postulated transition to our current universe using so-called metamaterials, structures in which the propagation of light can be precisely controlled. Experiments on such structures, they say, could test predictions that a “big flash” of radiation would accompany changes in the structure of spacetime that may have occurred in the early universe.

Over the past decade, theorists have learned that choosing the microscopic electric and magnetic properties of materials lets them manipulate light in surprising ways, potentially leading to devices like perfect lenses and invisibility cloaks. Experimentalists have begun to confirm these ideas using metamaterials–large arrays of tiny wires, rings, and other structures that are small compared to the light’s wavelength.

The tailored materials could also be used to explore unusual geometries of spacetime, say Igor Smolyaninov of the University of Maryland, College Park, and Evgenii Narimanov of Purdue University in West Lafayette, Indiana. Ordinarily, for a light wave going through a material, as the wavelength gets shorter, its frequency goes up, and this applies equally in all directions. But Smolyaninov and Narimanov describe a metamaterial where the relationship between frequency and spatial variations of electromagnetic fields is highly anisotropic. For some configurations of fields, you could increase the effective wavelength in one specific direction, and yet the overall frequency would go down.

The team shows that this so-called hyperbolic relationship between spatial and time variations of electromagnetic waves is exactly the one that you would get in a spacetime that has two time dimensions and two space dimensions. One property of this geometry is that, for a given frequency, there is an infinite number of electromagnetic field arrangements, or modes, whereas in normal spacetime there could be many modes but not infinitely many.

Smolyaninov grants that the engineered behavior won’t allow weird things like time machines–a theoretical possibility with two time dimensions–because it occurs only over a limited range of frequency and is disrupted by energy losses that are neglected in the theory. But manipulating the material may still let experimentalists watch what happens when the geometry of spacetime changes dramatically. For example, if the many extra dimensions predicted by string theory suddenly “rolled up” in the early universe, leaving just three space dimensions, some theorists predict that a “big flash” of radiation would have been produced, somewhat similar to the big bang. The flash would have occurred because any energy in the infinity of modes in the higher-dimensional spacetime would suddenly be released.

Smolyaninov and Narimanov propose constructing a structure that includes sheets of thin wires of gallium, which becomes more conductive when it melts just above room temperature. They calculate that the melting will change the metamaterial from normal to hyperbolic, so experimenters could look for the big flash as it cools. “With metamaterials, you can model this transition experimentally,” Smolyaninov says.

Ulf Leonhardt, of the University of St. Andrews in Scotland says that lab models can be very informative for phenomena where people have no direct experience and therefore limited intuition. “If these systems can be built in the lab, and if they show this effect, then one can settle the controversy.” The proposed system “sounds interesting and practical,” he says. “The devil is in the details.”